This subject really interesting to read, thank you for mentioning it!
Found this in case anyone is interested in reading about it
Recently, I stumbled upon the 6:40+ hour YouTube video, “The Mongols - Terror of the Steppe.” You might like it https://www.youtube.com/watch?v=PdFwMDuAnS4
This timeline coincides with the Crusades with, which the article talks about at length. I find the Crusades fascinating because they've shaped the modern world in so many ways.
Dan Carlin (of Hardcore History fame) once said that why he cares about military history is it shapes the world. If you look at the lightbulb, it doesn't really matter who invented it. Somebody would've. But take the Battle of Marathon, which shaped the entire history of Western Europe as the Greeks repelled the Persians. History would've been completely different. Or how Cyrus II (IIRC) essentially saved Judaism by rebuilding the Temple. Without that, Judaism may well have died out and, with it, all the Abrahamic religions may never have existed.
So the Crusades are fascinating because they've often portrayed as a religious war but they were anything but. Religion was simply the excuse. Instead medieval powers wanted to control the Levant to enrich themselves.
The Crusades essentially created international banking, making the Knights Templar incredibly wealthy [1]. One wonders if this was a necessary condition to the rise of the mercantile class that eventually displaced feudalism and brought on capitalism.
But back to the French. It's interesting that they were fascinated with the Mongols with everything else that was going on. During this same period, the Eastern Roman Empire still existed and the Moors occupied the Iberian peninsula. In many ways, the Mongols were more distant whereas the Arab "threat" was closer and more real. So why the Mongols?
[1]: https://bigthink.com/the-past/knights-templar-crusades-finan...
Crusades in middle east started as an attempt of Eastern Roman empire (although they just called it Roman empire / Basileia Romaion) to recover from recent advances of Muslim invaders in Anatolia (modern Turkey). But turned into an overwhelmingly religious effort in the west. The first crusade especially was largely ill organized and chaotic affair. Where on one end of the spectrum you had nobles arriving with somewhat well equipped forces and idea of what to do, and on the other you had pilgrims, with whatever they just picked up in their hands and not answering commands of anyone, but their priest.
The economic side of things came into play after the process started and gradually became dominant. But it didn't start like it.
Finally. Interest of France in Mongols can be easily explained precisely by the influence crusades had on French and other Christian elites in Europe. The initial victory of 1st Crusade was followed by a series of setbacks. Muslims gradually begun to push crusaders out, the fact that crusaders started to fight amongst themselves helped a lot.
And then mongols arrived, almost from nowhere, crushed one of most powerful Muslim states at the time, and didn't stop there. It did seem like an immense opportunity, and in a way it was. If French, or someone else in Christendom, could convince khans that some form of cooperation is possible, or even better, if Mongols converted to Christianity, there would be a decent chance to not only save Jerusalem, but to move on to Egypt (still majority Christian).